Name: How Music is Made Up of Math
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Hear a jazz musician explain how an octave, fifth, and fourth relate to math.

Pythagoras saw a connection between math, music, and nature.

How Music is Made Up of Math

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Hear a jazz musician explain how an octave, fifth, and fourth relate to math.

Pythagoras saw a connection between math, music, and nature.

Physics & Math

How Music is Made Up of MathPublished: May 19, 2025NARRATOR: The ancient Greeks found three relationships between notes especially pleasing. Now we call them an octave, a fifth, and a fourth.ESPERANZA SPALDING: An octave is easy to remember because it's the first two notes of "Somewhere Over the Rainbow." A fifth sounds like this, or the first two notes of "Twinkle, Twinkle Little Star." And a fourth sounds like... You can think of it as the first two notes of "Here Comes the Bride."NARRATOR: In the sixth century BCE, the Greek philosopher Pythagoras is said to have discovered that those beautiful musical relationships were also beautiful mathematical relationships by measuring the lengths of the vibrating strings. In an octave, the string lengths create a ratio of two to one. In a fifth, the ratio is three to two, and in a fourth, it is four to three.ESPERANZA SPALDING: Seeing a common pattern throughout sound, that could be a big eye-opener of saying, "Well, if this exists in sound, and if it's true, universally through all sounds, this ratio could exist universally everywhere, right?" And doesn't it?NARRATOR: Pythagoreans worship the idea of numbers. The fact that simple ratios produced harmonious sounds was proof of a hidden order in the natural world, and that order was made of numbers, a profound insight that mathematicians and scientists continue to explore to this day.

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